CN107179688B - Power system reliability analysis method considering Monte Carlo state sampling truncation - Google Patents

Power system reliability analysis method considering Monte Carlo state sampling truncation Download PDF

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CN107179688B
CN107179688B CN201710476314.2A CN201710476314A CN107179688B CN 107179688 B CN107179688 B CN 107179688B CN 201710476314 A CN201710476314 A CN 201710476314A CN 107179688 B CN107179688 B CN 107179688B
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李四勤
刘宝柱
焦龙
刘晋
赵晓东
侯赞
任勇
张迪
刘刚
张仁和
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Shizuishan Power Supply Co Of State Grid Ningxia Electric Power Co
North China Electric Power University
Electric Power Research Institute of State Grid Ningxia Electric Power Co Ltd
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North China Electric Power University
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Abstract

The invention belongs to the technical field of reliability analysis of power systems, and particularly relates to a power system reliability analysis method considering Monte Carlo state sampling truncation, which comprises the following steps of 1, inputting power system element data; step 2, determining the initial state of the element; step 3, performing Monte Carlo simulation by adopting a state duration sampling method, and calculating the fault-free working duration and the fault repairing duration; step 4, carrying out network topology analysis on the s-th state, and judging whether the state s can be split into isolated islands or the system is completely stopped; if so, truncating the obtained system time sequence state sequence; step 6, additionally inserting a recovery control state, and turning to step 3; if not, judging whether the problem of network disconnection into island or system full stop occurs, if so, establishing a recovery control model, otherwise, judging whether the network state has the load shedding problem, and if so, establishing a correction control model; and resolving node load shedding amount and total system load shedding amount, and calculating the times and duration of each system state to obtain a reliability index.

Description

Power system reliability analysis method considering Monte Carlo state sampling truncation
Technical Field
The invention belongs to the technical field of power system reliability analysis, and particularly relates to a power system reliability analysis method considering Monte Carlo state sampling truncation.
Background
Power system reliability is a measure of the ability of a power system to supply power and electrical energy to power consumers without interruption, at acceptable quality standards and in required quantities. And (3) evaluating each reliability index of the researched system by using data such as system topology information, element reliability parameters and the like and adopting an analytical method (such as a state space method and the like) or a Monte Carlo simulation method.
In the reliability analysis method, the analytic method is more effective when the processing system is small in scale and has low requirements on complex operating conditions, and the calculated amount is exponentially increased along with the number of elements when the complex system is processed; the Monte Carlo method has the greatest advantage that the convergence speed is independent of the dimension of the problem, and the method is more suitable for evaluating the reliability problem of a large-scale high-dimensional system and/or a power system with complex operation conditions.
The state duration sampling method is commonly used for reliability analysis of power systems, and is a time sequence (sequential) Monte Carlo simulation method. The method is based on sampling the probability distribution of the component state duration, simulating in a time span according to a time sequence (the simulation time can reach millions of hours according to the requirement of research problems), and performing system analysis and reliability index calculation in each sampling state.
According to the principle of the state duration sampling method, the sampling is automatically terminated after reaching a given time, and belongs to timing truncation sampling data. The disadvantages of this sampling approach are: and the difference of each state in the system state analysis is not considered, load flow calculation or load shedding calculation (belonging to the correction control category) is carried out on each state by default, and then the reliability index is obtained through calculation. In fact, if the sampled state is disconnected into an island or most of the generator sets (even all the generator sets) are shut down, the sampled system is sometimes shut down for a long time, and the analysis of the system state at the moment is insufficient by load flow calculation or load shedding calculation alone, and the control process, namely the recovery of the control calculation content, which is necessary to be involved in system full stop or island connection must be considered. The content of the application is breakthrough and improvement of the existing sampling and reliability analysis method, which is the original design purpose of the invention and is different from the existing reliability evaluation method of the power system.
Disclosure of Invention
In order to accurately master the reliability level of the running state of the power system and explore an analysis method which better meets the actual running requirements of the system in the reliability evaluation of the power system, the invention provides a power system reliability analysis method considering Monte Carlo state sampling truncation, which comprises the following steps:
step 1, inputting element data of an electric power system required for load flow calculation and reliability calculation, setting a sampling state dynamic storage unit, a final sampling state dynamic storage unit and a total effective state counter, and initializing;
step 2, determining the initial state of each element in the system, and setting all the elements to be in the running state at the initial moment;
step 3, performing Monte Carlo simulation by adopting a state duration sampling method, sampling the state duration of each element according to the fault rate and the repair rate of each element, calculating the fault-free working duration and the fault repair duration which meet the exponential distribution, and setting the number of the primary system time sequence states as N;
step 4, taking the s-th state, if s is larger than N, turning to the step 8, otherwise, carrying out network topology analysis on the s-th state, and judging whether the state s can be split into an island or the system is completely stopped; if yes, turning to the step 5, and if not, turning to the step 7;
step 5, truncating the system time sequence state sequence obtained by the sampling, recording the number of the effective states obtained by the sampling as s, sequentially adding the wheel state sampling results into a final state dynamic storage unit, adding s into a total effective state counter, and emptying the sampling state dynamic storage unit;
step 6, additionally inserting a recovery control state in the final sampling state dynamic storage unit, and meanwhile, adding a total effective state counter + 1; turning to the step 3, carrying out the next round of sampling again;
step 7, performing fault analysis on each system state obtained by sampling to judge whether the problem of network disconnection into an island or system full stop occurs, if so, turning to step 8, otherwise, turning to step 9;
step 8, establishing a recovery control model, and recovering the system to an initial state: solving by taking the fastest load recovery as a target;
step 9, judging whether the network state has the load shedding problem, if so, establishing a correction control model: solving by taking the minimum load shedding amount as an objective function;
and step 10, resolving node load shedding amount and total system load shedding amount, and calculating the times and duration of each system state to obtain a reliability index.
The electric power system element data comprises network parameters, topological structure information, generator output power, time sequence load power data, element fault rate, repair rate and total reliability simulation time.
The method for calculating the fault-free working duration and the fault repairing duration comprises the following steps:
Figure BDA0001328341340000031
Figure BDA0001328341340000032
wherein, U1、U2∈[0,1]Respectively, uniformly distributed random numbers obtained in the monte carlo sampling.
And 8, solving by adopting a particle swarm algorithm in consideration of the power limit constraint, the climbing rate constraint and the bus voltage limit constraint of the unit.
And 9, considering an optimization planning model of generator output power limit constraint, line power flow limit constraint and node voltage limit constraint, and solving by adopting a particle swarm algorithm.
The invention has the beneficial effects that: the reliability analysis method of the invention considers the recovery control process of the whole power system after the complete stop or the existence of the network disconnection, the recovery control strategy considers the power failure time of the disconnection area, the reliability index statistics considers the contribution of different system states to the index, and the reliability index statistics is closer to the actual system occurrence scene; the simulation method adopts a state duration sampling method to carry out Monte Carlo simulation, and is provided with a dynamic storage unit for storing a sampling state and a dynamic storage unit for storing a final sampling state; the sampling state determines whether the sampling sequence is truncated according to whether network disconnection into an island or system full stop occurs; the sampling state is inserted into a recovery control state due to truncation; in the state analysis, the establishment and the solution of a recovery control model are considered; the method can more reasonably consider the influence of different sampling states, particularly the system full stop or network disconnection state and the recovery control thereof on the reliability, so that the reliability analysis result can comprehensively consider the process and efficiency of the correction control or recovery control scheme of different system states, and the reliability analysis conclusion is more reasonable and effective.
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FIG. 1 is a flow chart of the reliability assessment algorithm of the present invention.
Fig. 2 is a diagram illustrating the sampling result of the initial system state.
Fig. 3 is a diagram illustrating the sampling result of the system state after considering truncation.
Detailed Description
The embodiments are described in detail below with reference to the accompanying drawings.
A method for analyzing reliability of a power system considering monte carlo state sampling truncation, as shown in fig. 1:
step 1, inputting system element data, including data required by load flow calculation, such as network parameters, topological structure information, generator output power, time sequence load power data and the like; the element reliability data comprises an element failure rate lambda, a repair rate mu, a reliability simulation total time T and the like; setting and initializing a dynamic storage unit stateA () for saving the sampling state information, setting and initializing a dynamic storage unit stateB () for saving the final sampling state information, and setting a total valid state counter Ns_allSetting the initial value to be zero;
step 2, determining the initial state of each element in the system, and generally setting all the elements to be in the running state at the initial moment;
step 3, performing Monte Carlo simulation by adopting a state duration sampling method, performing state duration sampling on each repairable two-state element (generator, power transmission line and the like) according to the fault rate lambda and the repair rate mu of each element and formulas (1) and (2), and calculating the non-fault working duration tau meeting the exponential distribution1And fault repair duration τ2Setting the number of the initial system time sequence states as N, and additionally storing the initial state dynamic storage units StateA (1) -StateA (N) in sequence;
Figure BDA0001328341340000041
Figure BDA0001328341340000042
wherein, U1、U2∈[0,1]Respectively, uniformly distributed random numbers obtained in the monte carlo sampling.
Step 4, taking the s-th state, if s is larger than N, turning to the step 8, otherwise, carrying out network topology analysis on the s-th state; judging whether the state s can be disconnected into an island or completely stopped; if yes, go to step 6, if not go to step 7;
in the step 5, the step of the method is that,the sequence of the system time sequence obtained by the sampling is truncated, the number of the effective states obtained by the sampling is recorded as s, and the sampling results of the wheel states are sequentially added into a final state dynamic storage unit StateB (N)s_all)～StateB(Ns_all+ s), adding s to the total valid state counter, i.e. implementing Ns_all＝Ns_all+ s; while clearing StateA ();
step 6, in StateB (N)s_all) Additionally inserting a recovery control state, and a counter Ns_all＝Ns_all+ 1; turning to the step 3, carrying out the next round of sampling again;
step 7, performing fault analysis on each system state obtained by sampling to judge whether the problem of network disconnection into an island or system full stop occurs, if so, turning to step 8, otherwise, turning to step 9;
step 8, establishing a recovery control model, and recovering the system to an initial state: aiming at the fastest load recovery, solving by adopting a particle swarm algorithm in consideration of unit power limit constraint, climbing rate constraint, bus voltage limit constraint and the like;
step 9, judging whether the network state has the load shedding problem, if so, establishing a correction control model: taking the minimum load shedding amount as an objective function, considering an optimization planning model of generator output power limit constraint, line power flow limit constraint, node voltage limit constraint and the like, and solving by adopting a particle swarm algorithm;
and step 10, resolving node load shedding amount and total system load shedding amount, and calculating the times and duration of each system state to obtain a reliability index.
The specific embodiment is as follows:
first, Monte Carlo State sampling with truncation considered
The state duration sampling method proposed by this patent, which takes into account the truncation of the sampling state, is described by taking as an example the three-element system shown in fig. 2 and 3. The system is composed of A, B, C three elements, and the internal connection relationship can be series, parallel or series-parallel connection. At the sampling start time, it is generally set that all the elements are in an operating state at the initial time. The following steps are followed:
1. inputting three element data of a system, including data required by load flow calculation, such as network parameters, topological structure information, generator output power, time sequence load power data and the like; the element reliability data comprises an element failure rate lambda, a repair rate mu, a reliability simulation total time T and the like; setting and initializing a dynamic storage unit stateA () for saving the sampling state information, setting and initializing a dynamic storage unit stateB () for saving the final sampling state information, and setting a total valid state counter Ns_allSetting the initial value to be zero;
2. determining the initial state of each element in the system, and generally setting all the elements to be in an operating state at the initial moment;
3. monte Carlo simulation is carried out by adopting a state duration sampling method, and for each element, according to the fault rate lambda and the repair rate mu of each element and a formula
Figure BDA0001328341340000061
In the formula of U1、U2∈[0,1]Respectively, uniformly distributed random numbers obtained during Monte Carlo sampling, sampling the state duration of each element, and calculating the fault-free operation duration tau satisfying exponential distribution1And fault repair duration τ2Here, the number of the initial system time sequence states is N equal to 11, and the initial state dynamic storage units StateA (1) to StateA (11) are additionally stored in sequence;
4. taking each state obtained by sampling to perform network topology analysis, and switching to a system state calculation link if 11 states are analyzed; when the 3 rd state, namely s is 3, the system is completely stopped, the sequence of the system time sequence states obtained by the sampling is truncated, the number of the effective states obtained by the sampling is recorded as s is 3, the wheel-shaped state sampling results are sequentially added into the dynamic storage units StateB (1) -StateB (3) of the final states, and the s is 3 and is added into the counter of the total effective states, namely N is realizeds_all＝Ns_all+ 3; simultaneously emptying state information after StateA (4);
5. additionally inserting a recovery control state in StateB ()State stateB (4), simultaneous counter Ns_all＝Ns_all+1；
6. And the next round of sampling is performed again.
Secondly, each sampling state is analyzed and calculated
1. Load flow calculation
And performing system analysis of each sampling state by adopting an alternating current power flow method. In order to reduce the calculation amount, a rapid on-off power flow calculation strategy can be adopted.
2. Load shedding calculation
When the component is shut down so that the system does not meet the operating constraints, the power generation rescheduling is used to eliminate the out-of-limit of the system and avoid load shedding as much as possible. When the shear load is unavoidable, the amount of shear load should be minimized. At this point, the following optimal load shedding model can be established.
An objective function:
Figure BDA0001328341340000071
constraint conditions are as follows:
Figure BDA0001328341340000072
Figure BDA0001328341340000073
PGimin≤PGi≤PGimaxi∈NG
QGimin≤QGi≤QGimaxi∈NG
0≤PCi≤PDii∈NB
0≤QCi≤QDii∈NB
Sij≤Sijmax(Sk)i,j∈NB
wherein, PCiAnd QCiThe respective active and reactive load reduction of node i is usually achieved by proportional reduction of the active and reactive loads, i.e. PCi/QCi＝PDi/QDi；WiReflecting the importance degree of each node as a weight coefficient; pGiAnd QGiActive and reactive power output of a generator node i are respectively obtained; pGimax、PGimin、QGimaxAnd QGiminThe active and reactive output upper and lower limits of the generator node i are respectively; pDiAnd QDiRespectively the active and reactive loads of the load node i; skRepresenting the state of the system obtained by the k sample; sijIs the apparent power of the line in the system state, SijmaxIs SkLine ij under state delivers power limit; NB is the number of nodes, ND is the number of loads, and NG is the number of generators.
3. Recovery control calculation
The recovery control process is generally divided into three phases: black start stage, net rack reconstruction stage and load recovery stage. Restoring power to the load is performed throughout the process.
(1) Black start phase
The black start stage is a process of providing starting power to an adjacent thermal power plant with critical starting time limit by a black start power supply to recover the generating capacity and re-grid connection. The black start power supply generally selects a unit with self-starting capability in the power network, such as a conventional hydroelectric generating set, a pumped storage unit, a gas turbine, a power support of an external system, an isolated subsystem after disconnection, and the like. The recovery process at this stage comprises: starting a black start power supply, charging related recovery paths (including a transformer, a line and the like), starting large auxiliary machines of a power plant, connecting a started unit to a grid, putting a certain amount of load to ensure the stable operation of the system and the like. The black start stage generally takes 0.5-1 h.
(2) And network frame reconstruction stage
The goal of the network frame reconstruction stage is to recover the main power unit and the main network frame, and mainly relates to network structure, generator starting sequence, recovery path optimization and the like. The whole process generally lasts for 3-4 hours. The following net rack recovery model with load recovery as the target can be established, and the particle swarm optimization algorithm is adopted for solving.
An objective function of inputting important loads first and inputting secondary loads as required:
Figure BDA0001328341340000081
and (3) constraint:
Figure BDA0001328341340000082
Figure BDA0001328341340000083
PGimin≤PGi≤PGimaxi∈NG
QGimin≤QGi≤QGimaxi∈NG
Vimin≤Vi≤Vimaxi∈NB
PLi-TLiXi≤0i∈NL
in the formula, L1And L2Important loads and general loads; x is the number ofiAnd xj0 or 1, representing whether or not a load is input, α and β each representing a weight coefficient indicating a difference in importance, k and l each representing the number of loads, and PLiAnd TLiRespectively representing the active power and the power limit value, X, of the lineiAnd 0 or 1, indicating whether the line is selected by the reconstruction process.
(3) Load recovery phase
The goal of the load recovery phase is to recover the load as quickly and as much as possible. At the moment, the actual running state of the system, the constraints of checking frequency, voltage and the like are considered, and the optimal load recovery amount of each recovery operation is determined; and then, determining a load input sequence and an overall recovery strategy according to factors such as the load location, the size and the importance degree of the nodes. This process typically lasts several hours. A load recovery optimization model can be established, and a particle swarm optimization algorithm is adopted for solving.
The objective function of the primary load input and the secondary load input according to the requirement is as follows:
Figure BDA0001328341340000091
and (3) constraint:
fmin≤f(xili)
Pmin≤∑(xili)
Vset≤Vtr
Vimin≤Vi≤Vimax
0≤Sij≤Sijmax
in the formula, f (x)ili) Representing the lowest value of the system frequency at the time of recovering the load point; pminRepresenting the minimum stable output of the current grid-connected unit; vtrRepresenting a transient voltage; the last 2 constraints represent the node voltage constraint and the line power constraint at steady state.
Thirdly, calculating the reliability index
The reliability index calculation adopts classical reliability indexes, including:
(1) desired power shortage indicator EENS (MWh/a)
Figure BDA0001328341340000092
Wherein, CiThe load shedding amount, MW, of the system state i; t is tiDuration of system state i, T total time of simulation analysis, and S set of all load shedding states.
(2) Load shedding probability index PLC
Figure BDA0001328341340000093
(3) Load shedding times index EFLC (times/a)
Figure BDA0001328341340000094
Wherein N isiIs the number of system states with load shedding.
(4) Average load shedding duration ADLC (h/time)
Figure BDA0001328341340000101
From the foregoing discussion, it can be seen that the power system reliability analysis method proposed by the present invention, which considers the monte carlo state sampling truncation, is original. The method can more reasonably consider the influence of different sampling states, particularly the system full stop or network disconnection state and the recovery control thereof on the reliability, so that the reliability analysis and calculation result is more reasonable, and the method is an effective, feasible and practical method.
The above embodiments are only preferred embodiments of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are also within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (5)

1. A power system reliability analysis method considering Monte Carlo state sampling truncation is characterized by comprising the following steps:
step 1, inputting element data of an electric power system required for load flow calculation and reliability calculation, setting a sampling state dynamic storage unit, a final sampling state dynamic storage unit and a total effective state counter, and initializing;
step 2, determining the initial state of each element in the system, and setting all the elements to be in the running state at the initial moment;
step 3, performing Monte Carlo simulation by adopting a state duration sampling method, sampling the state duration of each element according to the fault rate and the repair rate of each element, calculating the fault-free working duration and the fault repair duration which meet the exponential distribution, and setting the number of the primary system time sequence states as N;
step 4, taking the s-th state, if s is larger than N, turning to the step 8, otherwise, carrying out network topology analysis on the s-th state, and judging whether the state s can be split into an island or the system is completely stopped; if yes, turning to the step 5, and if not, turning to the step 7;
step 5, truncating a system time sequence state sequence obtained by sampling the state duration, recording the number of effective states obtained by the sampling as s ', sequentially adding the wheel-state sampling results into a final-state dynamic storage unit, adding s' into a total effective-state counter, and emptying the sampling-state dynamic storage unit;
step 6, additionally inserting a recovery control state in the final sampling state dynamic storage unit, and meanwhile, adding a total effective state counter + 1; turning to the step 3, carrying out the next round of sampling again;
step 7, performing fault analysis on each system state obtained by sampling to judge whether the problem of network disconnection into an island or system full stop occurs, if so, turning to step 8, otherwise, turning to step 9;
step 8, establishing a recovery control model, and recovering the system to an initial state: solving by taking the fastest load recovery as a target;
step 9, judging whether the network state has the load shedding problem, if so, establishing a correction control model: solving by taking the minimum load shedding amount as an objective function;
and step 10, resolving node load shedding amount and total system load shedding amount, and calculating the times and duration of each system state to obtain a reliability index.
2. The method of claim 1, wherein the power system component data includes network parameters and topology information, generator output power, time series load power data, component failure and repair rates, and total time to reliability simulation.
3. The method of claim 1, wherein the non-failure operation duration and the failure recovery duration are calculated by:
Figure FDA0002316643190000021
Figure FDA0002316643190000022
wherein, U1、U2∈[0,1]Respectively, uniformly distributed random numbers obtained in the monte carlo sampling.
4. The method according to claim 1, wherein the step 8 is performed by a particle swarm optimization in consideration of a unit power limit constraint, a ramp rate constraint and a bus voltage limit constraint.
5. The method according to claim 1, wherein the step 9 considers an optimization planning model of generator output power limit constraint, line current limit constraint and node voltage limit constraint, and adopts a particle swarm algorithm for solving.
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